This paper sets out the results of mathematical modeling and numerical simulations of the off-design (part-load) operation of the solid oxide fuel cell hybrid system (SOFC-HS). The governing equations of SOFC-HS modeling are given. An adequate simulator of the SOPC stack was made and described. The performance of the SOFC-HS with part- and over-load operation is shown, and adequate maps are given and described. The ranges of possible system operation conditions are determined. (C) 2006 International Association for Hydrogen Energy. Published by Elsevier Ltd. All rights reserved.